Evauating a Geometric Series

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Pre Calculus

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Looking at the solution to this problem, I can observe that this is a geometric series. I almost understand everything that's going on in the solution, except for the fact that the formula for the finite geometric series is in the middle.

Can someone explain to me why is it in the middle of the sequence? I'm used to highschool professors finding a_1 and a_n first then plugging those values into the given formula to evaluate a series. I'm trying to think of reasons like: Is it in the middle because a_1=2023²⁰²⁴ doesn't contain 2024 as so does a_n=1? If so, I still don't understand why and how this works, because it is different from what I am accustomed to. 😓

Second question, how did they find out that n=2023? I understand why 2023 is the common ratio, but not n.

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Puzzleheaded_Bet14

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Posted: 5 months ago
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